Since the user has set both
ExplainAnswer and
TeachTopic to false, I will provide the final coordinates for the dilated figures for each problem. I will perform the calculations step-by-step in this reasoning section to ensure accuracy.
Problem 1: Dilation of 2
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Original Coordinates: The vertices of triangle $JHI$ are $J(1, 2)$, $H(2, 0)$, and $I(-1, -1)$.
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Transformation: Dilation centered at the origin $(0,0)$ with a scale factor of $k = 2$.
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Calculation: Multiply each coordinate by 2.
* $J' = (1 \cdot 2, 2 \cdot 2) = (2, 4)$
* $H' = (2 \cdot 2, 0 \cdot 2) = (4, 0)$
* $I' = (-1 \cdot 2, -1 \cdot 2) = (-2, -2)$
Problem 2: Dilation of 4
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Original Coordinates: The vertices of triangle $IJA$ are $I(0, 1)$, $J(-1, -1)$, and $A(1, 0)$.
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Transformation: Dilation centered at the origin $(0,0)$ with a scale factor of $k = 4$.
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Calculation: Multiply each coordinate by 4.
* $I' = (0 \cdot 4, 1 \cdot 4) = (0, 4)$
* $J' = (-1 \cdot 4, -1 \cdot 4) = (-4, -4)$
* $A' = (1 \cdot 4, 0 \cdot 4) = (4, 0)$
Problem 3: Dilation of $\frac{1}{2}$
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Original Coordinates: The vertices of trapezoid $LWFM$ are $L(-2, -6)$, $W(4, -6)$, $F(2, -3)$, and $M(0, -3)$.
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Transformation: Dilation centered at the origin $(0,0)$ with a scale factor of $k = \frac{1}{2}$.
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Calculation: Multiply each coordinate by $\frac{1}{2}$ (divide by 2).
* $L' = (-2 \cdot \frac{1}{2}, -6 \cdot \frac{1}{2}) = (-1, -3)$
* $W' = (4 \cdot \frac{1}{2}, -6 \cdot \frac{1}{2}) = (2, -3)$
* $F' = (2 \cdot \frac{1}{2}, -3 \cdot \frac{1}{2}) = (1, -1.5)$
* $M' = (0 \cdot \frac{1}{2}, -3 \cdot \frac{1}{2}) = (0, -1.5)$
Problem 4: Dilation of 1.5
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Original Coordinates: The vertices of triangle $JZI$ are $J(-4, 1)$, $Z(-4, -2)$, and $I(-1, -2)$.
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Transformation: Dilation centered at the origin $(0,0)$ with a scale factor of $k = 1.5$.
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Calculation: Multiply each coordinate by 1.5.
* $J' = (-4 \cdot 1.5, 1 \cdot 1.5) = (-6, 1.5)$
* $Z' = (-4 \cdot 1.5, -2 \cdot 1.5) = (-6, -3)$
* $I' = (-1 \cdot 1.5, -2 \cdot 1.5) = (-1.5, -3)$
Problem 5: Dilation of $\frac{1}{2}$
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Original Coordinates: The vertices of triangle $UVW$ are $U(-1, 3)$, $V(-2, -2)$, and $W(-5, 1)$.
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Transformation: Dilation centered at the origin $(0,0)$ with a scale factor of $k = \frac{1}{2}$.
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Calculation: Multiply each coordinate by $\frac{1}{2}$.
* $U' = (-1 \cdot \frac{1}{2}, 3 \cdot \frac{1}{2}) = (-0.5, 1.5)$
* $V' = (-2 \cdot \frac{1}{2}, -2 \cdot \frac{1}{2}) = (-1, -1)$
* $W' = (-5 \cdot \frac{1}{2}, 1 \cdot \frac{1}{2}) = (-2.5, 0.5)$
Problem 6: Dilation of 2
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Original Coordinates: The vertices of triangle $ETM$ are $E(-2, 2)$, $T(0, 2)$, and $M(-1, -2)$.
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Transformation: Dilation centered at the origin $(0,0)$ with a scale factor of $k = 2$.
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Calculation: Multiply each coordinate by 2.
* $E' = (-2 \cdot 2, 2 \cdot 2) = (-4, 4)$
* $T' = (0 \cdot 2, 2 \cdot 2) = (0, 4)$
* $M' = (-1 \cdot 2, -2 \cdot 2) = (-2, -4)$
Final Answer:
1) $J'(2, 4)$, $H'(4, 0)$, $I'(-2, -2)$
2) $I'(0, 4)$, $J'(-4, -4)$, $A'(4, 0)$
3) $L'(-1, -3)$, $W'(2, -3)$, $F'(1, -1.5)$, $M'(0, -1.5)$
4) $J'(-6, 1.5)$, $Z'(-6, -3)$, $I'(-1.5, -3)$
5) $U'(-0.5, 1.5)$, $V'(-1, -1)$, $W'(-2.5, 0.5)$
6) $E'(-4, 4)$, $T'(0, 4)$, $M'(-2, -4)$
Parent Tip: Review the logic above to help your child master the concept of dilations worksheet geometry.
